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Probabilistic evaluation of time series models : a comparison of several approaches

Broecker, J., Engster, D. and Parlitz, U. (2009) Probabilistic evaluation of time series models : a comparison of several approaches. Chaos, 19 (4). ISSN 1089-7682

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Official URL: http://dx.doi.org/10.1063/1.3271343

Abstract/Summary

Several methods are examined which allow to produce forecasts for time series in the form of probability assignments. The necessary concepts are presented, addressing questions such as how to assess the performance of a probabilistic forecast. A particular class of models, cluster weighted models (CWMs), is given particular attention. CWMs, originally proposed for deterministic forecasts, can be employed for probabilistic forecasting with little modification. Two examples are presented. The first involves estimating the state of (numerically simulated) dynamical systems from noise corrupted measurements, a problem also known as filtering. There is an optimal solution to this problem, called the optimal filter, to which the considered time series models are compared. (The optimal filter requires the dynamical equations to be known.) In the second example, we aim at forecasting the chaotic oscillations of an experimental bronze spring system. Both examples demonstrate that the considered time series models, and especially the CWMs, provide useful probabilistic information about the underlying dynamical relations. In particular, they provide more than just an approximation to the conditional mean.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
ID Code:29156
Publisher:American Institute of Physics

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